Interlaminar contact resistivity and its influence on eddy currents in carbon fiber reinforced polymer laminates

Accepted Manuscript Interlaminar contact resistivity and its influence on eddy currents in carbon fiber reinforced polymer laminates Xiaojuan Xu, Hongli Ji, Jinhao Qiu, Jun Cheng, Yipeng Wu, Toshiyuki Takagi PII:

S0963-8695(17)30189-5

DOI:

10.1016/j.ndteint.2017.12.003

Reference:

JNDT 1939

To appear in:

NDT and E International

Received Date: 24 March 2017 Revised Date:

28 November 2017

Accepted Date: 17 December 2017

Please cite this article as: Xu X, Ji H, Qiu J, Cheng J, Wu Y, Takagi T, Interlaminar contact resistivity and its influence on eddy currents in carbon fiber reinforced polymer laminates, NDT and E International (2018), doi: 10.1016/j.ndteint.2017.12.003. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

ACCEPTED MANUSCRIPT

Interlaminar contact resistivity and its influence on eddy currents in carbon fiber reinforced polymer laminates Xiaojuan Xua, Hongli Jia*, Jinhao Qiua, Jun Chengb, Yipeng Wua, Toshiyuki Takagic State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China b School of Electric and Automation Engineering, Nanjing Normal University, Nanjing 210016, China c Institute of Fluid Science, Tohoku University, Sendai, Miyagi 980, Japan * Corresponding author: Hongli Ji (e-mail: [email protected]).

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Abstract: In this study, contact resistivity of interlaminar interface and its influence on eddy currents in carbon fiber reinforced polymer (CFRP) laminates were thoroughly investigated. Measurements of the contact resistivity between

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the adjacent laminae were conducted experimentally, together with the anisotropic bulk conductivity of a single-layer lamina. The measured values were then used in finite element (FE) models to study the influence of the contact resistivity on eddy currents in CFRP laminates. It was found that eddy currents are highly concentrated around the

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laminae interfaces when contact resistivity is taken into account, while the currents experience a steep drop in a non-contact model. The FE results were verified by comparing the calculated voltages with the experimentally measured ones. In addition, effects of electrodes size on the electric potential in CFRP were numerically analyzed. It was observed that electric potential diffuses due to the electrical anisotropy in CFRP, and thus the visible electrodes area is not the effective one.

1. Introduction

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Keywords: Contact resistivity; CFRP; Eddy current; Electrodes size.

Carbon fiber reinforced polymer (CFRP) is featured by its superior characteristics over metallic component such as light weight, robustness, damage tolerance, and fatigue and corrosion resistance. And thus it is being increasingly

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used as structural components and functional composites in many applications. For applications of composites, like damage detection using electric potential change [1-9], eddy current testing (ECT) [10], induction heating [11-14] and electromagnetic compatibility [15], it is important to comprehensively understand the electric properties.

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There are different methods for measuring the electrical conductivity of CFRP. The direct current (DC) four-probe and DC six-probe techniques [16] have been used to determine the conductivities of composites in longitudinal, transverse and thickness directions, and the resistance change curves under tensile load were also investigated. A contactless ECT method [17-19], based on the principle of electromagnetic induction, was applied to investigate the bulk electrical conductivities in both unidirectional and multidirectional laminates. The results showed that cross-ply laminate has much better electrical conductance than unidirectional plate. H. Menana et. al. [20] have done numerical analysis and used a rotating eddy current sensor to characterize the global electrical conductivity in a CFRP composite. Similarly, rotation of a couple of transmitter and receiver (T-R) coils was employed to characterize the in-plane fiber directions according to the electrically conductive fibers [10]. Their works showed that the probe signal reaches to a local maximum value in the fiber direction. Additionally, numerical modeling and experimental studies were also applied to define the anisotropic conductivity tensor of a CFRP material [19, 21-23]. Furthermore, 1 / 16

ACCEPTED MANUSCRIPT some other methods exploiting the fibers’ alternating current (AC) or DC conductivities as the detection principles have been proved to be effective in monitoring damages in CFRP [24]. All of the above previous researches on the electric properties emphasize bulk conductivity of the through-thickness direction. But bulk conductivity of composite materials is affected by the interlaminar electrical behavior [13, 14], which demonstrates the influence of fibers contact between adjacent laminae on bulk conductivity.

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Since through-thickness bulk conductivity is the summation of the bulk conductivity of each lamina in this direction and the contact resistivity across each interlaminar interface of CFRP, direct measurement of interfacial contact resistivity should be conducted rather than that of bulk resistivity of CFRP for the purpose of understanding interfacial electrical behavior. Wang and Chung measured the contact resistivity and investigated the effect of temperature [25], moisture [26], damage [27-29], curing pressure [30, 31] on the contact resistivity. The results

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showed that contact resistivity is lower for cross-ply than unidirectional CFRP laminates [32]. And in that reference, the lower contact resistivity was attributed to the fact that fibers of adjacent laminae press on to one another much more strongly for cross-ply than unidirectional laminates. But so far, to the authors’ knowledge, few researchers put

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their attention on interlaminar electrical behavior and effects of interfacial contact resistivity on eddy currents in composite materials, which should help to give a comprehensive understanding of the phenomenon that the bulk conductivity of CFRP laminates with different layer-up sequences varies considerably in reference [17], and the current density distribution in the through-thickness direction does not show a local maximum value at the top surface in CFRP laminate in reference [33].

In this work, contact resistivity of interlaminar interface and its influence on eddy currents in CFRP laminates

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were thoroughly investigated. Interlaminar contact resistivity and anisotropic conductivity were experimentally measured, and the effects of electrodes size on the electric potential in CFRP were discussed in Section 2. Section 3 numerically analyzed the interlaminar electrical behavior and the eddy currents in CFRP laminates based on the measured values. Section 4 conducted the corresponding experiments to verify the results in Section 3. Concluding

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remarks were drawn in the last part.

2. Measurement of anisotropic conductivity and contact resistivity

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A practical composite material is a pileup of several laminae, and each lamina contains serpentine and randomly distributed fibers orientated in the same direction. The fiber-fiber contacts always exist in CFRP laminates because of the curved fibers. The fiber-contact-network brings finite electric resistance in both transversal (90° direction) and through-thickness (z direction) directions. Therefore, conventional measurement of bulk resistivity contains both of the lamina bulk resistivity and the fiber contact resistivity. In this section, contact resistivity between adjacent laminae and anisotropic conductivity of a single-layer lamina were measured. Additionally, effects of electrodes area on the accuracy of the measured parameters were numerically analyzed.

2.1 Sample manufacture and electrodes configuration Carbon fiber composites used in this study are carbon fiber/epoxy sheet USN12500 and the gel content is 33%. In order to cure prepreg slice, the as-prepared prepregs were cut into small rectangular sheets of desired size. The 2 / 16

ACCEPTED MANUSCRIPT tailored sheets were then pressurized and cured in a vacuum drying oven (DZF-6090) with a hot press at 130°C for 90 min, and the curing pressure is 0.15 MPa. Three types of unidirectional single-ply samples were fabricated for measuring the anisotropic electric conductance (see Fig. 1). Figs. 1(a)-(c) show the electrodes configuration for measuring anisotropic conductivity in the fiber direction σ0, in the transversal direction σ90 and in the through-thickness direction σz, respectively. The other three types of two-layer laminates were manufactured for

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determining the contact resistivity, as shown in Fig. 2. The designed lay-up sequences are unidirectional (UD) [0/0] (Fig. 2(a)), angle-ply (AP) [0/45] (Fig. 2(b)) and cross-ply (CP) [0/90] (Fig. 2(c)), respectively, and all the manufactured laminates are in the same size with an in-plane dimension of 40 mm×40 mm.

Anisotropic conductivity of the three directions related to frequency are measured directly using impedance analyzer (HP4294A). Schematics of the sample configurations are shown in Figs. 1(a)-(c), respectively. The surfaces

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on which the silver paste was to be made were polished with sand paper to eliminate the superficial insulating resin layers until carbon fibers were completely exposed, and then silver paste was painted to achieve an intimate contact between the carbon fibers and the electrodes. After that, the silver paste was dried and conventional lead wires were

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placed on the electrodes. Silver paste was used here again for fixing the wire at the electrodes. After this, the electrodes were covered with epoxy resin to protect these electrodes. In order to measure the conductance in the three directions, the electrodes are placed on different locations. Two electrodes were located at the ends of the sample for measuring the longitudinal conductivity σ0, depicted as Fig. 1(a). Two different configurations, where the electrodes were seated either on the cut edges or on its top and bottom surfaces of the sample, were employed to measure the transversal σ90 and the through-thickness σz conductivities, denoted as Fig. 1(b) and (c), respectively. The reason why

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the silver electrodes are covered with whole surface will be explained in the end of this section.

2.2 Measurement results and discussion

As shown in Fig. 1, a constant current with a stabilized power supply was injected through the two electrodes,

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thus the voltage drop across the sample can be obtained using a voltmeter. According to the Ohm’s law, the resistance between the two electrodes can be calculated through the voltage drop as R=∆V/I. Thus, anisotropic resistivity can be

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calculated by using the following equation

ρ = RA l

(1)

where A is the electrodes area in the direction of current flow, and l is the distance between two electrodes. By using the reciprocal of resistivity σ=1/ρ, we can get anisotropic conductivity in the three directions, as in Table 1. It is easy to see that, although measured value of conductivity σ0 is significantly larger than that of σ90 and σz, σ90 and σz are not zero. These nonzero values are caused by the more or less fiber-fiber contact networks. Fig. 2 shows the other three well-fabricated plate samples for determining contact resistance, where the prepregs are stacked in different sequences to investigate the effect of the fiber direction difference on the contact resistivity. Similar to the configuration of measuring resistance in the through-thickness direction (see Fig. 1(c)), an impedance analyzer (Agilent 4294A) was used to determine the contact resistance. According to the series circuit theory, the contact resistance Rc can be obtained by subtracting the resistance R of single-layer sample in the through-thickness 3 / 16

ACCEPTED MANUSCRIPT direction from the total resistance Rt of two-layer laminates in the through-thickness direction (i.e. Rc=Rt-2R). Once the contact resistance Rc is obtained, the contact electrical resistivity ρco can be calculated by ρ co = ∆ R × S

(2)

where S is the electrodes area. The calculated contact resistivities of different laminates are listed in Table 1. Note

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that all measured values in Table 1 contain the resistance in a particular direction and the additional resistances of the wires and the electrodes. Due to the use of the silver paste, the additional resistances between the electrodes and the sample and that between the electrodes and the wires are negligible. Table 1

Anisotropic conductivity and contact resistivity for various composites. Contact resistivity ρco (Ω·m2)

σ0 = 29940

ρco in laminates [0/0]

9.28×10-5

σ90 = 4.8

ρco in laminates [0/45]

5.60×10-5

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Anisotropic conductivity σ (S/m)

ρco in laminates [0/90]

σz = 1.1

3.52×10-5

As illustrated in Table 1, the contact resistivity is found to be higher for UD than AP and CP composites. This is consistent with the experimental observation obtained by Wang et al. [31, 32]. Although the curing pressure for the unidirectional sample in Refs. [31] and [32] is 0.42 MPa higher than that of any cross-ply samples and the thickness of unidirectional turns out to be the lowest, the contact resistivity of the unidirectional one was the second highest

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rather than being the lowest. In the current study, the curing pressure for the sample in all composites is 0.15 MPa lower than that of the samples (0.19 MPa, 0.33 MPa and 0.42 MPa, respectively) in Refs. [31] and [32], and thus the obtained contact resistivities of the UD and CP samples in the references are lower than that in this work. A reasonable explanation of this phenomenon is that the larger curing pressure greatly increases the proximity of the

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fibers, as explained in Ref. [32], and this proximity may allow tunneling of the electrons across the epoxy-resin between the fibers on the two sides of the interlaminar interface. Hence, the obtained lower values of contact resistivity demonstrates the fact that the higher fiber content provides every fiber with more chances to contact the

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fibers of the other ply during composite fabrication. In addition, it is found that the direction differences of fibers from adjacent laminae plays a critical role in affecting the interfacial contact resistivity. The larger the direction error is, the lower the contact resistivity is. And thus the contact resistivity of the CP sample is the smallest, the measured value of the UD is the highest and the value of the AP sample is the median. The above results support the notion that the curing pressure forces the fibers of adjacent plies to press on to one another in CP sample and thus every fiber at the interlaminar interface contacts many fibers of the other layer (see Fig. 2(c)). While in the UD sample, the pressure provides little chance for every fiber to contact with others form the adjacent layer, because the fibers of one layer just sank into the other layer at the layer-layer interface (see Fig. 2(a)). It concludes that the higher the contact resistivity is, the smaller the extent of direct contact between fibers of neighboring plies is. In other words, the number of fiber-fiber contact points between adjacent laminae is less for UD sample than the other two samples. Therefore, a new numerical model is needed to 4 / 16

ACCEPTED MANUSCRIPT characterize the electrical behavior of interlaminar interface and investigate the effect of the interlaminar electrical behavior on the eddy currents in CFRP laminates. The details are in Section 3. In the process of experimental measurements, authors discovered that the electrodes areas will greatly affect the measurement accuracy due to the electrical anisotropy of CFRPs. To explain this phenomenon and estimate the measurement error caused by the electrodes size, FE analyses were performed using COMOSL Multiphysics.

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Different sizes of the electrodes were considered and the calculated resistance values were compared with those obtained by MATLAB based on resistance calculation formula (R=ρl/A). Taking the resistance in the through-thickness direction of a single-ply for example, the FE model is shown in Fig. 3, where the 0° fiber direction is parallel to the x-axis. The top and bottom surfaces of the central area are designed as the electrodes, where the sizes of the electrodes are 10 mm×10 mm, 16 mm×16 mm, 20 mm×20 mm, 28 mm×28 mm, 30 mm×30 mm and 40

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mm×40 mm respectively.

Fig. 4 shows the distribution of electric potential V in the unidirectional single-layer model. Figs. 4(a), (b) and (c) represent the numerical results with different electrodes sizes. In Fig. 4, the electric potential distribution is not

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limited in electrodes zones marked as the black solid boxes. It stretches out along the fiber direction, demonstrating the fact that the ratio of longitudinal conductance and transversal conductance is very large. For assessment of the relative error introduced by the change of the electrodes sizes, Fig. 5 shows the calculated resistance values under different situations. The horizontal axis denotes different electrodes sizes, while the vertical axis denotes the calculated resistance in the through-thickness direction. As shown in the figure, the solid line marked with solid square corresponds to MATLAB results (i.e. electrodes size is the same as model in-plane size), the dash

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line marked with solid triangle corresponds to FE results using entire area (i.e. electrodes size equals to model size), and the solid line marked with filled circle corresponds to FE results using part area (i.e. electrodes size is changeable at the central blue area, see Fig. 3). As Fig. 5 shows, resistance values obtained in simulation analyses using entire area agreed well with MATLAB results. While FE simulations using part surfaces as electrodes area fail to give the

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same results as those from the other two cases.

The resistances significant difference between the last case and the former two cases is due to the difference of the real electrodes areas. For the former two cases, the surfaces size is the electrodes area, and thus there is no

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potential diffusion and the electrodes area is the effective area. While in the last case, the effective area is not the electrodes size marked as black solid rectangular (see in Fig. 4) but the actual diffusion area. If the marked area was used as the effective area to calculate the resistance, it would result in an overestimation of resistance value due to the misused electrodes area. Moreover, the smaller the silver paste is, the larger the relative error (between resistances obtained from the visible electrodes area and the effective one) is. The relative error between resistances obtained from the visible electrodes area and the effective one, in the last case, reaches up to 55.69% when the electrodes area is 10 mm×10 mm. And the relative error between the visible electrodes area and the effective one is about 22.1% when the electrodes area is 30 mm×30 mm. Therefore, the electrodes size in measuring electrical resistance should be seriously considered.

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ACCEPTED MANUSCRIPT 3. Numerical studies and results In this section, the authors mainly focus on numerically analyzing interfacial electrical behavior and its influence on eddy current and induced voltage. To tackle those issues, two interface conditions in FE models are considered. In the first case, fibers of the adjacent laminae are in contact and the contact resistivity was defined using the measured ones from Section 2. In the second case, the fibers are supposed to be not in contact.

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3.1 Numerical model

FE simulations were carried out to study the influences of contact resistance on eddy currents induced in CFRP laminates. The FE model setup is shown in Fig. 6, which composes of 8 thin layers with each ply thickness of 0.125 mm. Nine FE models respectively named S1-S9 listed in Table 2 were established. For each model in the first case

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(fibers contact), every two adjacent layers are connected by a surface contact resistance [34]. The values of the contact resistivity, which are relate to the fibers direction on the two sides of the interlaminar interface, were given in Table 1 in Section 2. An air-cored pancake coil was established with 0.5 mm lift-off (from the top plate surface to the

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bottom surface of coil), and the coil parameters are tabulated in Table 3. Based on the magnetic vector potential A and the electric scalar potential φ , basic governing equation of the A- φ method is written as following (jωσ - ω 2 ε ) A + µ − 1∇ × ∇ × A + (σ + jωε ) ∇ φ = J e

(3)

where ω and σ are the angular frequency and conductivity, respectively. Parameters ε and µ are permittivity and permeability, respectively. Vector Je is the external current density for coil excitation. A boundary condition of

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n×A=0 is imposed on the external boundary of the domain. Each lamina in the model was simulated individually and regarded as a homogeneous and anisotropic sheet, and the conductivity tensor is generally represented by the following equation [21].

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σ 0 − σ 90   2 2 sin(2θ ) 0 σ 0 cos (θ ) + σ 90 sin (θ ) 2   σ 0 − σ 90 2 2  σ = σ 0 sin (θ ) + σ 90 cos (θ ) 0  sin(2θ )   2  0 0 σ z    

(4)

where θ is the fiber direction of the ply with respect to x-axis. σ0, σ90 and σz are given in Table 1, respectively. Table 2

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sequence of specimens.

Designed number

Stacking sequences

S1

0°8

S2

0°4/90°4

S3

0°2/90°4/0°2

S4

45°2/0°2/-45°2/90°2

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ACCEPTED MANUSCRIPT 0°2/90°2/0°2/90°2

S6

45°/0°/-45°/90°2/-45°/0°/45°

S7

45°/0°/-45°/90°/45°/0°/-45°/90°

S8

0°/90°/0°/90°2/0°/90°/0°

S9

0°/90°/0°/90°/0°/90°/0°/90°

S10

[-45°/0°/45°/90°]6

Table 3 Coil parameters and test conditions. Inner diameter: 1.2 mm Outer diameter: 3.2 mm Height: 0.8 mm

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Coil parameters

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S5

Numbers of turns: 140

Exciting current: 20 mA Frequency: 440 kHz

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Test conditions

Lift-off: 0.5 mm (from the top surface of model to the bottom surface of coil)

For models in the second case (no fibers contact), it is supposed that there is no fiber-fiber contact networks across the designed interface, and the specific adjacent laminae are separated from each other by an inserted electric insulation [34] governed by Equation (5)

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n⋅J = 0

(5)

where n is the unit normal vector, and J is the induced current density. The rest of the interfaces are the same configuration as the fibers contact case.

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To describe the extent of the influence of contact resistance, induced voltage of the EC probe above the conductor is investigated. The z component of magnetic flux density Bz is used to calculate the voltage. According to

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Faraday’s law, the induced voltage V can be expressed as follows V = jω N ∫∫ B z dxdy

(6)

where ω is angular frequency, N is coil turns. Moreover, a simulation model without the conductor should be made to get the voltage variation, and thus the electrical conductivity of the model is set to zero. Therefore, the voltage variation caused by the conductive sample can be evaluated by subtracting the voltage without plate from the one with plate. ∆ V = V withplate − V withoutplate

(7)

3.2 Currents distribution in CFRPs considering fibers contact Numerical results of eddy current distribution in CFRP models S1, S7, and S9 are shown in Figs. 7(a)-(i), where 7 / 16

ACCEPTED MANUSCRIPT the marked arrows represent the current flow direction. All the current densities drawn in the figures are extracted at the 2nd interface between the 2nd ply and the 3rd ply. As shown in Fig. 7, the eddy currents distributed in the three models are different from each other. Figs. 7(a)-(c) illustrate the distribution of Jx, Jy, and Jz in sample S1. As shown in the figure, the amplitude of Jx is much bigger than Jy because of the much higher conductivity along the fibers than transverse to the fibers. Also

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due to the higher ratio of σL/σT, distribution path of the currents Jx and Jy is of a shape of a narrow ellipse, where the two components are stretched in the fiber direction and tightened in the transversal direction. The lower density of Jz is related to the lower conductivity in the through-thickness direction, and it performs dual variation in both x and y directions.

The currents distribution in S7 at the 2nd interface shown in Figs. 7(d)-(f) are close to that in S9, except for Figs.

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7(e) and (h). It is observed from these images that the current distribution is sensitive to the direction difference of the fibers on the two sides of the interface, where the currents are stretched in two directions (0° and -45°, or 90° and 0°). This is because that the fibers of the two plies tend to press on to one another during curing process. If the fibers

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on the two sides of the interfaces are not parallel, the substantial fiber-fiber contact networks across the interlaminar interface occurs, which is corresponding to the lower contact resistivity value in Table 1. Therefore, the induced current stretches along the contacted fibers via the contact points in S7 and S9. While in S1, fibers in all plies are parallel to each other, and the fibers just sink into the adjacent plies to some extent during curing, which indicates relatively few fiber-fiber contacts and results in high contact resistivity value.

Actually, contact between randomly twisted fibers may occur and results in substantial conductive networks

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across the interlaminar interfaces in microscopic scale. Hence, in macroscopic scale, a brief closed circuit can be used to explain the currents enhancement phenomenon. A schematic of these closed circuits are shown in Figs. 8(a) and (b) for both samples S7 and S9, respectively, and the four crossing points in each figure represent the fibers contact points. Case (a) corresponds to the 0°/45° plies, and case (b) corresponds to the 0°/90° plies. As shown in the

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figures, the closed current loops become conductive paths for the induced currents, and hence a considerable current density is gathered around and across the interface due to the fiber-fiber contacts. Therefore, a larger eddy currents were induced in S7 and S9 compared with S1. Meanwhile, the amplitude of the induced current is directly related to

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the contact resistance. The lower the contact resistance is, the greater the extent of fiber-fiber contact networks is, and hence the larger the current density around the interface is. Based on the contact resistivity values of S7 and S9 in Table 1, the amplitude of Jx in Fig. 7(g) is larger than that in Fig. 7(d). Furthermore, the significant difference between the two components Jy in Figs. 7(e) and (h) is resulted from the relative direction of the fibers on the two sides of the interface. Note that the current density Jy in Figs. 7(e) and (h) represents the top surface of the 3rd -45° ply in S7 and the top surface of the 3rd 0° ply in S9. Thus amplitude of the current density Jy in Fig. 7(e) is much larger than that in Fig. 7(h). For unidirectional CFRP, however, as discussed in Section 2, fibers of UD sample have little chance to contact each other during curing pressure, which eventually leads to the higher contact resistivity. Due to the same fibers direction in UD sample, there is no closed circuit across the interface, and thus induced currents can only flow in one direction as shown in Figs. 7(a)-(b). 8 / 16

ACCEPTED MANUSCRIPT To further explain the aforementioned observations and to visualize the results at all interfaces, additional snapshots of the current density of Jx and Jy in xz cross section for plates S1, S2 and S9 are plotted in Fig. 9. In the figures, it was found that the current density does not show a maximum at the top surface of S2 and S9, but reaches to local maximum around all interfaces, except for that case in S1. Although so far authors could not clarify the complicated physical background in CFRPs, it is predicted that the strong anisotropy in electric conductivity of the

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CFRPs and the interaction of the accumulated electric charge between adjacent orthogonal layers through the contact points may result in the significant current increase around the interfaces. However, the accumulated charge has little contribution to the current increase in S1 because of the same fibers direction on the two sides of the interfaces. A case in which the current density is highly concentrated at the interfaces between adjacent orthogonal layers has been reported [13, 17, and 33]. Furthermore, as shown in Fig. 11, the current density does not reach a maximum close to

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the interfaces between 0°/90° plies in the case of fibers noncontact, but shows a sharp decrease around the interfaces. This is because the accumulated charge cannot interact with each other between adjacent layers due to no contact point across the interfaces. It furtherly proved that fibers contact plays a remarkable role in affecting the eddy

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currents induced in CFRPs.

3.3 Currents distribution in CFRPs with non-contact case

Simulation results of the current density in CFRPs with no fiber-contact is shown in Fig. 10, wherein Figs. 10(a)-(c) indicate the eddy current induced in S7 at the 2nd interface. It is worth noting that the non-contact case leads to the current repartition and the repartition domain depends on the shape of electric insulation area (marked as

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the rectangular frames in the figures). In the case of non-contacts in Fig. 10, eddy current components Jx and Jy are stretched along only one direction near the interface, rather than in two directions shown in Figs. 7(d)-(i). As for the models with electric insulation, there is no closed conductive circuits across the interfaces due to the non-contact fibers, and thus the induced current cannot flow across the interface between two adjacent laminae. Apart from this, a

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square hole was found to exist in the contour plot of Jz distribution, which means that zero-current can flow through the boundary and forces the normal component of the induced current to be zero.

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3.4 Comparison and discussion

Corresponding to the above numerical analyses, contact resistivity has a remarkable influence on the interfacial electric behavior, which causes a high concentration or a steep attenuation of the current density around the interfaces. In this part, curves of the current density along the through-thickness direction of CFRPs with different contact resistivity are quantitatively compared in Fig. 11, which includes the contact and non-contacts results from S2 and S9. The abscissa is the z coordinate from the top surface of the sample to the bottom surface, and the ordinate is the electric current density. Obviously, the current density is found to be highly focused around the interfaces between 0°/90° plies when the actual fibers contact was considered, as shown in Figs. 11(a) and (c). However, a significant decline of the current density takes place at the interfaces when the electric insulation was applied, as shown in Figs. 11(b) and (d), which means that there is no fibers contact due to the resin-rich interlayer. This is consistent with the fact that the resin-rich interlayer is capable of impeding current flowing across the interlaminar interface, thus 9 / 16

ACCEPTED MANUSCRIPT resulting in a sharp decrease in the current density around the interface. Significantly, eddy current density does not have the maximum value at the top surface (see Figs. 11(a) and (c)), even for the cross-ply sample S9 (Fig. 11(c)), when the contact resistance was considered in the model. While a remarkable maximum value can be found at the top surfaces in both samples of S2 and S9 (see Figs. 11(b) and (d)) when non-contact was considered. This is because fiber-contact through laminae enables the currents to flow across

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the interface, and thus it can lead to charge accumulation around the interface. On the contrary, electrical insulation corresponds to no fiber contact, and the non-contact interlayer impedes the currents flowing across the interface. And then the maximum value is located at the surface (see the current density envelope of S1 in Fig. 9(a)), according to skin effect of eddy current.

Furthermore, the induced voltage calculated by Equation (7) was extracted to characterize the electrical

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properties of the plates. Three simulation cases were considered to investigate the influence of contact resistivity on electrical conductivity of CFRP laminates:

Sim. case 1 (solid line with triangles): each interface is modeled using contact resistivity element as intact

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interface;

Sim. case 2 (solid line with squares): the 2nd interface is modeled using electric insulation node as non-contacts; Sim. case 3 (solid line with inverted triangles): the 2nd and 4th interfaces are modeled using electric insulation node as non-contacts.

All electric insulation areas are of the same size in the simulation model (100 mm×100 mm). The induced voltage curves corresponding to the three cases are plotted in Fig. 12. Compared with Sim. case 1, a noticeable

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decline of the voltage amplitudes can be found in both Sim. case 2 (except S1 and S2) and Sim. case 3 (except S1). When the electric insulation was inserted into the interface formed by two plies with a same fiber direction, the induced voltages remain almost unchanged (such as S1 and S2 in Sim. case 2 and S1 in Sim. case 3). A significant reduction of the induced voltage amplitudes can be found when the electric insulation was applied to the interface

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with adjacent laminae of different fiber directions, such as S3-S9 in Sim. case 2 and S2-S9 in Sim. case 3. As analyzed in Section 3.2, the induced current of one of the laminae cannot flow across the interface to the other lamina in a non-contacts case, such that the current density around the interface suddenly decreases.

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On the other hand, as illustrated in Figs. 7, 8 and 9, there occurs a current concentration phenomenon around the interface when fibers direction of the two sides of the interface is different from each other. Hence, a higher voltage value can be found in samples S2-S9, while a quite small induced voltage was found in S1 due to the same fiber direction. In addition, for samples S2 to S9, the one with more fiber directions did not always come with larger induced voltage. In the case of S3, S6 and S7, the contact resistance across ±45° plies is larger than that across 0°/90° plies, and thus the voltages of them are lower than that of S5, S8 and S9. Furthermore, it is noticeable that the electrical conductivities of the plates are also consistent with the number of the angled interface (formed by two adjacent plies arranged in different fiber directions). In comparison with sample S6, although the 0°/90° orthogonal plies were embedded in S5, the induced voltage signal observed in S5 is smaller than that in S6. The voltage variation, therefore, supports the notion that the contact resistivity has a critical influence on the 10 / 16

ACCEPTED MANUSCRIPT eddy currents in CFRP laminates and the detailed conclusions are as following: 1. Conclusion based on comparison of Sim. cases 1-3 is that fiber contacts can result in voltage rise. The more the fiber contacts, the less the contact resistivity is and the higher the voltage will be; 2. Conclusion based on comparison of S1-S9 in each case is that the angle between the fibers directions of adjacent layers affects the voltage remarkably. The bigger the angle is, the less the contact resistivity is and the higher

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the voltage will be.

4. Experimental validation and discussion

In this section, eddy current experiments were carried out to obtain the probe voltages. And then the numerically calculated voltages from Section 3 were compared with the experimental ones, in order to verify the existence of

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fibers contact cross each interlaminar interface and its influence on electric conductivity. In addition, detection experiment of interlaminar delamination was performed for multidirectional CFRP which is partially not in contact.

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4.1 Experimental procedures

As listed in Table 2, for determining electrical properties of the practical CFRP laminates, nine samples S1-S9 with different stacking sequences were fabricated using hand-made by laminating 8 tailored unidirectional prepregs (the same carbon fiber/epoxy sheets as used in Section 2) in different directions 0°, ±45° and 90°. Any two adjacent layers are stacking naturally under the curing pressure provided by a weight. The cured samples have a dimension of 100 mm×100 mm×1 mm as shown in Fig. 13(a). For detection delamination crack in CFRP laminate, the other

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sample S10 listed in Table 2 was designed. The configuration diagram of the sample fabrication is shown in Fig. 13(b). The prepared laminate was put between two heating platens of the hot press, and the temperature of the platens was increased from room temperature to 80°C for 30 min under a pressure of 2 MPa. Then it was continuously cured at 130°C for 2 h under a pressure of 12 MPa and subsequently cooled to room temperature automatically. Supporting

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jigs were placed on two sides of the sample to prevent excessive squeeze flow of the resin matrix. Before curing, a tailored insulation sheet with an in-plane size of 20 mm×20 mm was inserted into the 2nd interface between the 2nd layer and the 3rd layer to simulate the interlaminar delamination crack, which is located in the depth of 0.25 mm

mm.

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from the top surface as shown in Fig. 6(b). The well-done defect sample has a dimension of 300 mm×300 mm×3

An ECT approach based experimental system was employed to measure the induced voltage. The testing system includes a signal generator (Agilent 33220A), a stepping motor in X-Y plane, an A/D converter, a computer, an absolute-type probe (for characterizing electrical conductivity of the samples S1-S9) and a transmitter-receiver (T-R) probe (for detecting interlaminar delamination in sample S10), and a lock-in amplifier (Signal Recovery SR844, operational frequency from 25 kHz to 200 MHz), which allows extracting a weak useful signal buried in background noise. It outputs complex voltage comprising real part ∆VR and imaginary part ∆VI, and thus the induced voltage Vp of the probe can be expressed as Vp =

∆VR 2 + ∆VI 2

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ACCEPTED MANUSCRIPT Vp is then normalized by Vn=Vp/Vmax, where Vmax is maximum value of the voltage obtained from plate sample S9. The EC probe is placed on the centre area of the plates to avoid the edge effects [22]. Before each measurement, calibration of the probe against the tested samples should be made, and the probe signal should be set to 0 when it places in the air. Conventional ECT inspections operate at certain frequencies. However, the sensitivity of the probe voltage at a

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low-frequency is not enough for a CFRP composite material due to the low electrical conductivity. Meanwhile, the higher frequencies suffer from a greater susceptibility to liftoff, tilt and surface roughness, which cause higher levels of background noise. It is therefore important to explore an effective approach for maximizing the sensitivity of the ECT probe. Inspired by Liu [35, 36] and Hughes [37], the author operates the EC probes at a frequency close to its electrical resonant frequency, which can maximize the inspection sensitivity.

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A schematic of the absolute probe and T-R probe is presented in Figs. 14(a)-(b), where both of the probes consist of two coils and two coaxial cable leads with of 1 m length. In absolute probe, each coil comprises 605 turns around an air core, and the inner diameter is 2 mm and the outer diameter is 5 mm. The probe has a characteristic resistance

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in air of R0=37.5 Ω, inductance in air of L0=565±0.5 µH and the coaxial cable has a capacitance of C0=216 pF/m. Each coil of T-R probe comprises 140 turns, and the inner diameter and outer diameter are 1.2 mm and 3.2 mm, respectively. The characteristic parameter is R0=10.9 Ω, L0=32±0.5 µH and C0=109 pF/m. In order to determine the optimal frequency of the EC probes, a 4294A Agilent impedance analyzer and sweeping frequency method were used to find the characteristic signal of the probes. The impedance curves of the probes are plotted in Figs. 15(a) (dashed line, absolute probe) and 15(b) (dashed line, T-R probe) as a function of

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frequency, where the resonant frequencies of the absolute and T-R probe are about 456 kHz and 2.69 MHz, respectively. After then, the probes were driven respectively by an Agilent 33220A arbitrary function generator via the cable leads, and the frequency was swept from 0 kHz to 4 MHz. A sinusoidal ±0.5 V signal was used to create a swept voltage signal, and the voltage across the probes (probes voltage, V) at each frequency was then monitored and

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recorded. As shown in the figures (solid line), it is important to note that the probes voltage reaches to a maximum value at a specific frequency close to the impedance resonant frequency. This is because that the drive current reaches to a local minimum value at the resonance, while the impedance is maximum. And hence the resonant frequency shift

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results in obvious signal enhancing phenomenon. In this paper, the operating frequency of the absolute probe and T-R probe were set as 440 kHz and 2.48 MHz, respectively, in order to avoid the detrimental effects of environmental noise.

4.2 Results and discussion

The normalized signals obtained from both experimental measurements (Exp., dash line with dots) and numerical simulations (Sim. cases 1, 2 and 3) are shown in Fig.16. The specimens S1 - S9 shown in the abscissa is listed in Table 2. As plotted in the figure, the voltage signals obtained from Sim. case 1 are in good agreement with the Exp. voltage signals. The error between the results of Exp. and Sim. case 1 is due to some inevitable experiments uncertainties, such as cross-layer currents, the length of current paths [17], the fabrication of the test samples, liftoff and tilt of the probe, etc. 12 / 16

ACCEPTED MANUSCRIPT In contrast to Sim. case 1, significant deviations from Exp. voltage signals exist in both Sim. cases 2 and 3, because no fibers contact was considered across the designated interface. The more the number of the electrical insulation element is, the larger the deviation is. The agreement of Exp. and Sim. case 1 demonstrates the existence of fiber-fiber contacts in each interlaminar interfaces during the sample fabrication process of CFRPs. Since the interface electrical behavior has such a

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significant effect on the eddy currents, it cannot be neglected in eddy current testing for CFRPs. Considering the Point Spread Function (PSF) of a probe [38], a transmitter-receiver (T-R) probe was utilized to visualize delamination damage. Fig. 17 shows the experimental result of eddy current imaging performed for the 24-layer multidirectional laminate [-45/0/45/90]6 (S10) with an inserted delamination crack. As shown the figure, a significant voltage variation can be clearly observed in the simulated delamination zone. The shape and location of

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the existed damage can be obviously obtained as marked with the solid box in the experimental imaging. This is because that delamination results in a remarkable distortion on eddy currents distribution as shown in Fig. 10. Eddy

5. Conclusions

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current method is therefore a potential technique for delamination detection in CFRP.

This paper thoroughly analyzed the interfacial electrical behavior and its influence on eddy currents in composites of different layer-up sequences.

Firstly, in order to obtain the electrical parameter of each lamina and interface, the anisotropic conductivity of a single-layer lamina and the contact resistivity between adjacent laminae of different fiber directions were measured.

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The contact resistivity was found to decrease gradually with increasing angle difference between adjacent laminae. Additionally, it was observed that electrodes area influence the resistance measurements remarkably, which makes it difficult to calculate the resistance value correctly when the visible electrodes area are not the effective electrodes one. To eliminate the effect and determine the actual effective area, the relative error between the visible

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electrodes area and the effective one was numerically calculated with the aid of COMSOL and MATLAB. Results illustrated that when the visible electrodes area is less than the model surfaces, severe diffusion of the electric potential occurs along the fiber direction. And the relative error between resistances obtained from the visible

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electrodes area and the effective one reaches up to 55.69% when the visible electrodes area is 10 mm by 10 mm. The measured anisotropic conductivity and contact resistivity were then employed in FE models to detailedly investigate the interfacial electrical behavior and its influence on eddy currents in CFRPs. Numerical results indicated that the interfacial electrical behavior has a significant impact on the electric conductivity of CFRPs. The smaller the contact resistivity is, the larger the eddy currents grows, and the better the electric conductivity (depicted using probe voltages) becomes. For adjacent laminae with different fibre directions, visualization of the current distribution shows that the current density reaches to a local maximum value near the interfaces in the fibre contacts case, while the currents attenuate steeply around the interfaces in the non-contact case. For adjacent laminae with same fibre direction, the influence of fibre contacts between adjacent laminae on the electric conductivity is negligible. 13 / 16

ACCEPTED MANUSCRIPT Experiments were carried out to validate the numerical results. The good agreement between the experimental and the numerical results verifies that the effect of the interface electrical behavior on the eddy currents in CFRPs is significant, and thus the fiber contacts (contact resistivity) at laminate interfaces cannot be neglected for ECT in CFRPs. Furthermore, the experimental results clearly demonstrated that eddy currents technique can be used to detect delamination and an interlaminar delamination in 0.25 mm depth of a multidirectional CFRP has been detected

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successfully.

Acknowledgements

This work was supported by the Major State Basic Research Development Program of China (973 Program, No. 2015CB057501), the Fundamental Research Funds of the Central Universities (No. NP2016201), the Research Fund

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of State Key Laboratory of Mechanics and Control of Mechanical Structures (No. 0515Y02 & NE2015101), the “333” project of Jiangsu Province (No. BRA2015310) and the Priority Academic Program Development of Jiangsu Higher

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Education Institutions (PAPD).

References

[1] Todoroki A. Effect of number of electrodes and diagnostic tool for delamination monitoring of graphite epoxy laminates using electric resistance change. Composites Science and Technology 2001, 61:1871-1880. [2] Todoroki A. Monitoring of electric conductance and delamination of cfrp using multiple electric potential measurements. Advanced Composite Materials 2014, 23(2):179-193.

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[3] Todoroki A, Tanaka M, Shimamura Y. Measurement of orthotropic electric conductance of cfrp laminates and analysis of the effect on delamination monitoring with an electric resistance change method. Composites Science and Technology 2002, 62:619-628.

[4] Todoroki A, Tanaka Y. Delamination identification of cross-ply graphite/epoxy composite beams using electric

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resistance change method. Composites Science and Technology 2002, 62:629-639. [5] Todoroki A, Tanaka Y, Shimamura Y. Delamination monitoring of graphite epoxy laminated composite plate of electric resistance change method. Composites Science and Technology 2002, 62:1151-1160.

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[6] Angelidis N, Wei CY, Irving PE. The electrical resistance response of continuous carbon fibre composite laminates to mechanical strain. Composites Part A: Applied Science and Manufacturing 2004, 35(10):1135-1147.

[7] Park JB, Okabe T, Takeda N, et al. Electromechanical modeling of unidirectional cfrp composites uder tensile loading condition. Composite: Part A 2002, 33:267-275. [8] Abry JC, Choi YK, Chateauminois A, et al. In-situ monitoring of damage in cfrp laminates by means of ac and dc measurements. Composites Science and Technology 2001, 61:855-864. [9] Irving PE, Thiagarajan C. Fatigue damage characterization in carbon fibre composite materials using an electrical potential technique. Smart Materials and Structures 1998, 7:456-466. [10] Gerhard M, Rolf L, Ole K. Non-destructive characterisation of carbon-fibre-reinforced plastics by means of 14 / 16

ACCEPTED MANUSCRIPT eddy-currents. Composites Science and Technology 2001, 61:865-873. [11] Bensaid S, Trichet D, Fouladgar J. 3-d simulation of induction heating of anisotropic composite materials. IEEE Transactions on Magnetics 2005, 41(5):1568-1571. [12] Bensaid S, Trichet D, Fouladgar J. Electromagnetic and thermal behaviors of multilayer anisotropic composite materials. IEEE Transactions on Magnetics 2006, 42(4):995-998.

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[13] Wasselynck G, Trichet D, Ramdane B, et al. Interaction between electromagnetic field and cfrp materials a new multiscale homogenization approach. IEEE Transactions on Magnetics 2010, 46(8):3277-3280.

[14] Wasselynck G, Trichet D, Ramdane B, et al. Microscopic and macroscopic electromagnetic and thermal modeling of cfrps. IEEE Transactions on Magnetics 2011, 47(5):1114-1117.

[15] Christopher LH, Sarto MS, Johansson M. Analyzing carbon-fiber composite materials with equivalent-layer

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models. IEEE Transactions on Electromagnetic Compatibility 2005, 47(4):833-844.

[16] Park JB, Hwang TK, Kim HG, et al. Experimental and numerical study of the electrical anisotropy in unidirectional carbon-fiber-reinforced polymer composites. Smart Materials and Structures 2007, 16(1):57-66.

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[17] Cheng J, Ji HL, Qiu JH, et al. Role of interlaminar interface on bulk conductivity and electrical anisotropy of cfrp laminates measured by eddy current method. NDT & E International 2014, 68:1-12. [18] Li X, Yin W, Liu Z, et al. Characterization of carbon fibre reinforced composite by means of non-destructive eddy current testing and fem modeling. 17th World Conference on Nondestructive Testing 2008. [19] Yin WL, Withers PJ, Sharma U, et al. Noncontact characterization of carbon-fiber-reinforced plastics using

58(3):738-743.

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multifrequency eddy current sensors. IEEE Transactions on Instrumentation and Measurement 2009,

[20] Menana H, Féliachi M. Modeling the response of a rotating eddy current sensor for the characterization of carbon fiber reinforced composites. The European Physical Journal Applied Physics 2010, 52(2):1-5. [21] Pratap SB, Weldon WF. Eddy current in anisotropic composites applied to pulsed machinery. IEEE Transactions

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on Magnetics 1996, 32(2):437-444.

[22] Cheng J, Qiu JH, Takagi T, et al. Numerical analysis of correlation between fibre orientation and eddy current testing signals of carbon-fibre reinforced polymer composites. International Journal of Applied

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Electromagnetics and Mechanics 2012, 39:251-259. [23] Menana H, Féliachi M. Electromagnetic characterization of the cfrps anisotropic conductivity: Modeling and measurements. The European Physical Journal Applied Physics 2011, 53(2):1-5. [24] Kupke M, Schulte K, Schuler R. Non-destructive testing of frp by d.C. And a.C. Electrical methods. Composites Science and Technology 2001, 61:837-847. [25] Victor HG, Chung DDL. Interlaminar interface relaxation upon heating carbon fiber thermoplastic-matrix composite studied by contact electrical resistivity measurement. Composite Interfaces 2002, 9(6):557-563. [26] Wang SK, Chung DDL. Effect of moisture on the interlaminar interface of a carbon fiber polymer–matrix composite, studied by contact electrical resistivity measurement. Composite Interfaces 2002, 9(5):453-458. [27] Wang SK, Chung DDL. Mechanical damage in carbon fiber polymer-matrix composite, studied by electrical 15 / 16

ACCEPTED MANUSCRIPT resistance measurement. Composite Interfaces 2002, 9(1):51-60. [28] Wang SK, Chung DDL., Chung Jaycee H. Impact damage of carbon fiber polymer–matrix composites, studied by electrical resistance measurement. Composites Part A: Applied Science and Manufacturing 2005, 36(12):1707-1715. [29] Wang SK, Chung DDL. The interlaminar interface of a carbon fiber epoxy matrix composite as an impact sensor.

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Journal of Materials Science 2005, 40:1863-1867. [30] Wang SK, Kowalik DP, Chung DDL. Effects of the temperature, humidity, and stress on the interlaminar interface of carbon fiber polymer-matrix composites, studied by contact electrical resistivity measurement. The Journal of Adhesion 2002, 78(2):189-200.

[31] Wang SK, Kowalik DP, Chung DDL. Self-sensing attained in carbon-fiber–polymer-matrix structural

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composites by using the interlaminar interface as a sensor. Smart Materials and Structures 2004, 13(3):570-592. [32] Wang SK, Chung DDL. Electrical behavior of carbon fiber polymer-matrix composites in the through-thickness direction. Journal of Materials Science 2000, 35:91-100.

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[33] Mizukami K, Mizutani Y, Kimura K, et al. Detection of in-plane fiber waviness in cross-ply cfrp laminates using layer selectable eddy current method. Composites Part A: Applied Science and Manufacturing 2016, 82:108-118. [34] COMSOL AC/DC Module-User's Guide.

[35] Liu CY, Dong YG. Resonant enhancement of a passive coil-capacitance loop in eddy current sensing path. Measurement 2012, 45(3):622-626.

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[36] Liu CY, Dong YG. Resonant coupling of a passive inductance-capacitance-resistor loop in coil-based sensing systems. IEEE Sensors Journal 2012, 12(12):3417-3423. [37] Hughes R, Fan Y, Dixon S. Near electrical resonance signal enhancement (nerse) in eddy-current crack detection. NDT & E International 2014, 66:82-89.

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2011, 57(3):227-236.

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[38] Mook G, Michel F, Simonin J. Electromagnetic imaging using probe arrays. Journal of Mechanical Engineering

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Interlaminar contact resistivity and its influence on eddy currents in carbon fiber reinforced polymer laminates Xiaojuan Xua, Hongli Jia*, Jinhao Qiua, Jun Chengb, Yipeng Wua, Toshiyuki Takagic State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China b School of Electric and Automation Engineering, Nanjing Normal University, Nanjing 210016, China c Institute of Fluid Science, Tohoku University, Sendai, Miyagi 980, Japan * Corresponding author: Hongli Ji (e-mail: [email protected]).

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a

(a)

(b)

(c)

Fig.1. Configuration schematic of electrodes for measuring the anisotropic conductivity in the three directions: (a) σ0; (b) σ90; (c)

(b)

(c)

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(a)

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σz .

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Fig.2. Prepregs configuration for determining contact resistivity: (a) [0/0] plate; (b) [0/45] plate; (c) [0/90] plate.

Fig.3. FE model to investigate the effect of electrodes sizes on the accuracy of the measured resistance.

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(a)

(b)

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(c)

Fig.4. Distribution of the electric potential in the unidirectional single-layer sample covered with different electrodes sizes: (a)

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10mm×10mm; (b) 20mm×20mm; (c) 30mm×30mm.

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Fig.5. Comparison of the obtained resistance values from FE simulation and MATLAB calculation considering different

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electrodes sizes.

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Fig.6. (a) Geometry schematic of an analytical model for CFRP laminate; (b) profile of the laminate and coordinate system.

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(g)

(e)

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(d)

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Fig.7. Numerical results of x, y and z-directional components of current density distributed in 2nd interface. (a)-(c): on the top surface of the 3rd ply in sample S1; (d)-(f): on the top surface of the 3rd ply in sample S7; (g)-(i): on the top surface of the

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3rd ply in sample S9.

(a)

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Fig.8. Current loops formed in: (a) 0/45 plies; (b) 0/90 plies.

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w

(b)

(d)

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(a)

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Fig.9. Curren density of Jx and Jy in xz plane, (a)-(b): in sample S1; (c)-(d): in S2; (e)-(f): in sample S9.

(a)

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(c)

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(f)

Fig.10. Current distribution of Jx, Jy and Jz caused by non-contact at 2nd interface: (a)-(c) on the top surface of the 3rd ply in

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sample S7; (d)-(f) on the top surface of the 3rd ply in sample S9.

(b)

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Fig.11. Comparison of Jx and Jy in the through thickness direction considering: (a) actual fibers contact and (b) non-contact in sample S2; (c) actual fibers contact and (d) non-contact in sample S9.

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Fig.12. Induced voltage of specimens S1-S9. Sim. case 1: all interfaces are with fiber contact; Sim. case 2: only the 2nd interface

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is with no fiber contact; Sim. case 3: only the 2nd and 4th interfaces are with no fiber contact.

Fig.13. Experimental samples: (a) CFRP laminate for determining electrical properties; (b) CFRP laminate with a simulated

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inserted delamiantion.

(a)

(b)

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Fig.14. Eddy current probes: (a) absolute-type probe; (c) transmitter-receiver probe.

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frequency shift of the probe voltage.

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Fig.16. Normalised experimental and numerical voltage obtained from specimens S1-S9.

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Fig.17. Experimental imaging of interlaminar delamination with size of 20×20mm2 in laminate [-45/0/45/90]6.

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